Calculation Of Effective Thermal Conductivity Research Articles

Pore structure characterization and effective thermal conductivity modeling of fibrous building thermal insulation materials based on X-ray tomography

The existing structural characterization methods of building materials as well as thermal conductivity calculation models can not be directly applied when considering fibrous building thermal insulation materials with intricate skeletons. In this study, rock wool is considered the research object, and the X-ray tomography method is used to characterize the pore structure and extract structural parameters. Based on the actual pore morphology of the material, the pores in the representative elementary volume (REV) are reasonably assumed to be cubic. Additionally, considering the contact thermal resistance of fibers and the randomness of pore distribution, the curved pattern of heat conduction pathway with the ever-changing diameter is reasonably simplified into a series-parallel form of the curved heat chain with the same diameter. On this basis, the fractal models of effective thermal conductivity are established in horizontal and vertical directions. Finally, a modified formula for the effective thermal conductivity calculation of fiber thermal insulation materials is proposed, taking into account the influence of fiber orientation on the material thermal conductivity. It was shown that the relative deviation between the calculated correction value and the experimental value of the effective thermal conductivity is all less than 16.13%.

Numerical estimation of effective thermal conductivity of reconstructed 2D structures of cement-based building materials

Cement-based building materials are fundamental for constructing modern buildings, and accurate determination of their thermal conductivity is crucial for calculating building energy consumption. In this study, random growth theory is used to reconstruct the two-dimensional pore structures of cement-based building materials in different forms. Furthermore, heat transfer simulations and calculations of effective thermal conductivity based on the finite element method are conducted for these pore structures. The effect of pore structure parameters on the effective thermal conductivity of cement-based building materials is investigated by this method. The results indicate that porosity, pore size, and the degree of pore regularity can all influence the effective thermal conductivity of cement-based building materials. At a porosity of 0.3, the fluctuations in the effective thermal conductivity caused by variations in pore sizes and degrees of pore regularity are most drastic.

CFD modeling of crystallization fouling with CO2 desorption incorporated for a falling-film evaporator in thermal desalination

Seawater flowing around horizontal tubes in falling-film evaporators is a common configuration for thermal desalination. Heat is transferred from in-tube steam condensation to the shell-side seawater by conduction through the tube wall and scaling layer, and conduction and convection to the evaporating liquid film. CO2 is simultaneously released from seawater and mixed with the produced vapor. Fouling coupled with CO2 desorption has deleterious impacts on both evaporation and condensation. The evaluation of spatiotemporal dependent crystallization fouling and CO2 desorption is vital to selecting optimal operating conditions. In this work, a CO2 desorption model is integrated into CFD modeling for predictions of coupled heat and mass transfer, to understand and predict scale formation and CO2 desorption with local and transient profiles of temperature, carbonate species concentrations, pH, and total alkalinity. The porosity of the scale layer is experimentally determined as 67.7 % and invoked in the calculation of effective thermal conductivity. The simulation results reveal that high steam temperatures increase seawater total alkalinity and accelerate scale formation. The scale thickness on the bottom tube reaches 0.30 μm and 5.24 μm for steam temperatures of 60 °C and 80 °C, respectively. High salinity leads to a large CO2 desorption rates. The CO2 desorption rate increases 43 % when the seawater salinity increases from 35 to 55 g/kg. The effects of operating conditions on carbonate speciation and pH have been compared and analyzed. This model can serve as a comprehensive tool for the design of thermal desalination systems and optimal operation.

X‐ray Computed Tomography Characterization of Slag Crust and the Effect of Bubbles and Metallic Iron in Slag on Heat Transfer to Copper Stave

Understanding the heat transfer properties of the slag crust is critical to the safe operation of copper staves. The distribution of metallic iron and bubbles in the slag crust is detected by X‐ray computed tomography. The thermal conductivity of the slag crust is modified based on an effective thermal conductivity model and laser thermal conductivity measurements to predict the effect of metallic iron and bubbles on the heat transfer in the slag crust. The results show that the average volume fractions of metallic iron and air bubbles in the slag crust are 3% and 4.5%, respectively. The measured value is consistent with the trend of the effective thermal conductivity calculation model, and the calculation result of the Maxwell–Eucken effective thermal conductivity model is very accurate. Variations in the volume fraction of metallic iron in the slag crust have a greater effect on the thickness of the slag crust, while variations in the volume fraction of bubbles have a smaller effect on the thickness of the slag crust. It is recommended to keep it between 10 and 30 mm in blast furnace production to help improve the operational life of the copper stave.

Structural modeling and calculation of thermal conductivity of polyimide composite materials

Issues of direct modeling effective thermal conductivity of two-component thermally conductive polyimide composite films based on polyimide thermosetting varnishes and thermally conductive powder fillers are considered.
 3D-structural modeling of elementary cubic cells of polyimide composites has been performed.
 Calculations of average heat fluxes and effective thermal conductivity of variants of polyimide composite films with the introduction of highly thermally conductive highly dispersed and ultradispersed powder fillers into the polyimide matrix were carried out, including those from SiO2, SiC, Al2O3, AlN, taking into account boundary and initial conditions using COMSOL MULTIPHYSICS software.
 Specific recommendations are proposed for direct modeling of the thermal conductivity of environments with a complex structure and for carrying out with sufficient reliability numerical calculations of the effective thermal conductivity of polyimide composite films in order to increase their thermal conductivity from 0,12 W/(m•K) up to 1-4 W/(m•K) by changing concentration and thermal conductivity of mixtures of filler particles of micron and ultramicron sizes.

Study on the theoretical calculation method for the effective thermal conductivity of carbon nanotube composite molten salt for solar energy application

Carbonate salt is a potential heat storage material for solar thermal power. Aimed at calculating the effective thermal conductivity of Li 2 CO 3 -K 2 CO 3 eutectic doped with carbon nanotube (CNT), a theoretical calculation method based on the three-dimensional random curl structure model was developed. Meanwhile, for the purpose of method verification, CNT composite molten salt was prepared by high-energy ball grinding method. The curl degree of carbon nanotube was determined by image identification technique. The effective thermal conductivity of the composite molten salt was measured to validate the calculation model. The comparison showed that, for well-mixed CNT composite molten salt, the error of the theoretical calculation model was less than 8.5%, which indicated that this calculation model can be used to calculate the effective thermal conductivity of CNT composite molten salt. Moreover, the influence of key factors such as the curl degree and aspect ratio of CNT on the effective thermal conductivity of composite molten salt were revealed. The results included that, first, the effective thermal conductivity ( λ eff ) of composite molten salt decreased with increasing CNT curl degree. Second, increasing CNT aspect ratio to 175 could improve λ eff of composite molten salt. Third, the increase of CNT thermal conductivity was the key factor to the improvement of λ eff of composite molten salt. Fourth, λ eff of the composite molten salt could be significantly increased when the order of magnitude of the interfacial thermal resistance (m 2 ·K·W −1 ) was reduced to 10 −7 . • A calculation model on λ of CNT enhanced molten salt for heat storage is given. • Curl phenomenon of carbon nanotube is quantified via image identification. • 3-D random curl structure physical model is established. • Carbon nanotube enhanced salt is prepared by ball milling method and tested. • Effective thermal conductivity calculation is validated with experiments.

Experimental investigation on thermal conductivity of clay-bearing sandstone subjected to different treatment processes: Drying, wetting and drying II

The influence of dry-wet change process on rock thermal conductivity is the key to many geological and engineering issues, especially for rocks with high clay mineral content. In this study, sandstone with different clay mineral contents were subjected to different treatment processes, namely drying, wetting and drying II, and their thermal conductivity were measured through the hot wire method. The results indicate that the thermal conductivity of the samples subjected to the drying II treatment was significantly lower than that of the samples subjected to the drying treatment, and the magnitude of the decrease was related to the clay mineral content in the samples. Moreover, using the effective thermal conductivity calculation model that considers microcracks, it is found that the main reason for the decrease in the thermal conductivity of sample is the large number of secondary cracks generated in sample during the wetting-drying process. According to the pore structure and the microstructure of the samples under different state, it is speculated that the dissolution of soluble minerals, disintegration of minerals, swelling and shrinking of clay minerals are the possible causes of cracks in the sample during the wetting-drying process.

Effective Thermal Conductivity Calculation and Measurement of Litz Wire Based on the Porous Metal Materials Structure

Litz wires are employed in high-frequency electrical machines due to their advantages of reducing the ac losses, including minimizing the skin effect and the proximity effect. In order to improve the reliability of such machines, and enable accurate thermal predictions at the design stage, accurate calculation of the thermal conductivity of litz wire is important. In this paper, a calculation method based on the Gasar porous metal materials model is put forward. In this method, a cell model is extracted from the litz wire, and a thermal resistance network is used to calculate the equivalent thermal conductivity (ETC). Following this, two finite-element analysis (FEA) models for the same litz wire are built, one with actual thermal conductivities for the different constituent materials and another with the calculated equivalent thermal conductivity for an equivalent material, with the two models showing similar thermal characteristics. Finally, an experimental setup is built for measuring the steady-state ETC of litz wire. The apparatus structure and characteristics are described in detail, and the experiment uncertainty and measurement errors are analyzed. Three types of litz wire are measured in the experimental, and the results from experiment and calculation are consistent.

Determining efficient values for the thermophysical properties of bulk materials

A procedure has been devised for determining the effective thermophysical properties of bulk materials with different granulometric and material composition, based on the integration of discrete and continuous models of media. The problem on the mechanical-thermal state of a cylindrical layer of bulk material has been stated in order to determine its effective thermophysical properties. Based on the discrete-continuous perceptions of bulk media, an approach has been suggested and a procedure has been devised for solving the problem set. The algorithm for determining effective values of thermophysical properties of bulk materials has been constructed. Numerical implementation of the developed procedure was performed using free open source software (LIGGGHTS, ParaView). The proposed procedure makes it possible to determine effective values for the thermophysical properties of a bulk material (bulk density, effective thermal conductivity coefficient and the effective value for isobaric mass heat capacity) with arbitrary material and granulometric composition. In this case, there is a need for a minimum volume of complex and costly experimental studies with subsequent numerical simulation of the process of the mechanical-thermal state of the examined bulk material. In this case, the true physical properties can be acquired from reference books. Using an example of model material, its effective thermophysical properties have been defined for different granulometric composition and the verification of the developed procedure has been performed. It was established that data on the effective thermal conductivity calculation based on the devised procedure differ from data obtained based on the theoretical averaged dependences, within 0.8‒9.0 %. The reported results are useful for numerical analysis in the continual approximation of thermal modes of the processes and equipment where bulk materials are used

Artificial neural network-based prediction of effective thermal conductivity of a granular bed in a gaseous environment

Artificial neural network (ANN), a machine learning technique, is employed to predict the effective thermal conductivity of granular assemblies in the presence of a stagnant gas. ANN is trained with the help of estimated thermal conductivities calculated through resistor network (RN) model. RN model considers the effect of the presence of stagnant gas and the gas pressure (Smoluchowski effect) for the calculation of effective thermal conductivity. Granular assemblies are generated and compacted through discrete element method (DEM). The ANN is trained to predict the effective thermal conductivity of a granular assembly for a set of measurable experimental parameters (stress and packing fraction) without requiring the knowledge of microstructural details (coordination numbers and overlaps) of the assembly. The predicted effective thermal conductivity values through ANN are in good agreement with the experimental results. Estimation of effective thermal conductivity through the trained ANN is much faster (few seconds compared to few hours required for DEM together with RN approach) with very good accuracy.

Numerical prediction of effective thermal conductivity of ceramic fiber board using lattice Boltzmann method

Application of the lattice Boltzmann method has been extended for the analysis of combined transient conduction and radiation heat transfer through highly porous fibrous insulation media. Firstly, LBM has been employed for the analysis of combined mode of transient conduction radiation heat transfer in a 2 D rectangular enclosure containing an absorbing, emitting and scattering medium and results are compared with already published ones. The results have been found in good accord for different values of radiation-conduction parameter, scattering albedo and south (hot) wall emissivity. Furthermore, the proposed LBM for the calculation of effective thermal conductivity of ceramic fiber board has been employed. A random-generation growth method for generating micro morphology of natural ceramic fiber board has been selected. The conductive, radiative and effective thermal conductivity has been numerically estimated using the present LBM. It is found that the predicted effective thermal conductivity for different values of fibrous bulk density is in good agreement with the experimental data.

Comparative evaluation of heat conduction and radiation models for CFD simulation of heat transfer in packed beds

The existing major heat conduction and radiation models for packed bed of particles are reviewed and evaluated by comparing the predicted results with experimental data. For low-temperature condition, it is found that the Zehner-Bauer-Schlünder (ZBS) model is less sensitive to the effect of contact area and is thus recommended for the calculation of effective thermal conductivity of packed bed. For high-temperature condition, although numbers of models can be used to calculate the radiative heat transfer behavior in packed bed, the Breitbach and Barthels (B-B) correlation is the optimal method applicable for different particle diameters, emissivities and voidages. The results of CFD simulations using the identified optimal heat transfer models agree well with the thermal measurements by thermocouple in four coal pyrolysis fixed-bed reactors mounted with or without particularly designed internals.

An adaptive isogeometric boundary element method for predicting the effective thermal conductivity of steady state heterogeneity

This work presents an adaptive isogeometric boundary element method (IGBEM) for the calculation of effective thermal conductivity of steady state heterogeneities. Based on the generalized self-consistent scheme (GSCS), some integral equation formulations which only contain the unknown temperatures on the interface are used to calculate the effective thermal conductivity of steady state composites. In our approach, the geometries of the inclusion and original matrix are described using NURBS basis functions. The advantage over currently used methods is that no geometrical errors exist in the analysis process. And the geometry data in the isogeometric GSCS model can be taken directly from CAD programs. In addition, based on the upper bound of the relative error of the Gaussian quadrature formula, an adaptive integration method is used to compute the boundary integrals, which makes the computation of the integrals easier and more efficient at optimal computational cost. The comparisons between the results obtained by the present method and the existing counterparts are carried out and the good agreement can be observed.

State of the art of thermal characterization of electronic components using computational fluid dynamic tools

PurposeLatest Computational Fluid Dynamics (CFDs) tools allow modeling more finely the conjugate thermo-fluidic behavior of a single electronic component mounted on a Printed Wiring Board (PWB). A realistic three-dimensional representation of a large set of electric copper traces of its composite structure is henceforth achievable. The purpose of this study is to confront the predictions of the fully detailed numerical model of an electronic board to a set of experiment results to assess their relevance.Design/methodology/approachThe present study focuses on the case of a Ball Grid Array (BGA) package of 208 solder balls that connect the component electronic chip to the Printed Wiring Board. Its complete geometrical definition has to be coupled with a realistic board layers layout and a fine description of their numerous copper traces to appropriately predict the way the heat is spread throughout that multi-layer composite structure. The numerical model computations were conducted on four CFD software then compare to experiment results. The component thermal metrics for single-chip packages are based on the standard promoted by the Joint Electron Device Engineering Council (JEDEC), named JESD-51. The agreement of the numerical predictions and measurements has been done for free and forced convection.FindingsThe present work shows that the numerical model error is lower than 2 per cent for various convective boundary conditions. Moreover, the establishment of realistic numerical models of electronic components permits to properly apprehend multi-physics design issues, such as joule heating effect in copper traces. Moreover, the practical modeling assumptions, such as effective thermal conductivity calculation, used since decades, for characterizing the thermal performances of an electronic component were tested and appeared to be tricky. A new approach based on an effective thermal conductivity matrix is investigated to reduce computation time. The obtained numerical results highlight a good agreement with experimental data.Research limitations/implicationsThe study highlights that the board three-dimensional modeling is mandatory to properly match the set of experiment results. The conventional approach based on a single homogenous layer using effective thermal conductivity calculation has to be banned.Practical implicationsThe thermal design of complex electronic components is henceforth under increasing control. For instance, the impact of gold wire-bonds can now be investigated. The three-dimensional geometry of sophisticated packages, such as in BGA family, can be imported with all its internal details as well as those of its associated test board to build a realistic numerical model. The establishment of behavioral models such as DELPHI Compact Thermal Models can be performed on a consistent three-dimensional representation with the aim to minimize computation time.Originality/valueThe study highlights that multi-layer copper trace plane discretization could be used to strongly reduce computation time while conserving a high accuracy level.

해석 방법에 따른 창호-벽체 접합부의 결로 방지 성능 비교

The purpose of this paper is to compare calculation results of performances of condensation resistance of joints of windows and walls according to analysis standards, simulation programs, and modeling methods and also analyze the causes. Domestic and relevant foreign criteria were reviewed, and Heat transfer simulation was conducted targeting double and triple glass windows. Also, an improved modeling plan was proposed comparing performance of condensation Resistance depending on the modeling approach. The analysis results, from different calculation methods of effective thermal conductivity of cavity spaces showed significant differences in accordance with the analysis standards. It appeared that automatic calculation of effective thermal conductivity by ISO 15099 was impossible using Physibel Bisco. Therefore, an improved and simplified modeling method using respective heat transmission coefficients for window panes and frames was proposed. It was confirmed that compared to the simple modeling, the improved modeling method decreased errors of surface temperature on joints of windows and walls by up to 10% and compared to the detail modeling, all modeling cases were within 10% or less.

Contribution of waste products in single-layer ceramic building envelopes to overall energy savings

The contribution of waste materials to the overall energy savings in buildings with single-layer ceramic envelopes is twofold. They can not only enhance the thermal properties of the brick blocks but also reduce the total energy necessary for the brick production. In this paper the contribution of waste products to the energy performance is demonstrated for a typical brick family house in the climatic conditions of Prague, Czech Republic. The energy calculations are conducted using Energy Plus with pre-calculated parameters given by the PHPP model. Specific computational modules for the calculation of effective thermal conductivity of brick blocks are utilized as integral parts of the energy performance calculation tool. Five different types of external walls are analyzed. They are made of solid clay bricks, sawdust-lightweighted solid clay bricks and a new type of highly perforated ceramic block with improved geometry which was developed recently by a Czech brick producer in three versions, having the cavities filled with air, waste polyurethane and mineral wool. The obtained results show that perforating the bricks, together with lightening their body and applying thermal insulating cavity fillers, can reduce the specific heating demands of the analyzed building up to 79.4%.

A Monte Carlo simulation and effective thermal conductivity calculation for unidirectional fiber reinforced CMC

Due to the high thermal-mechanical performance, ceramic matrix composite (CMC) is regarded as an alternate material for high temperature components of aircrafts. The thermal conductivity of unidirectional CMC is sensitive to its microstructural characteristics. Herein, the Monte Carlo method is introduced to simulate the real distribution of fibers and air pores. The complete procedure is programmed by ANSYS Parametric Design Language and executed automatically. The effective thermal conductivity of this composite at room temperature is calculated. The effect of fiber arrangement as well as matrix porosity with different fiber fractions is studied. The statistic results are gotten and both longitudinal and transverse thermal conductivity are computed. The random arrangement of fibers can result in a deviation of transverse thermal conductivity in different calculation times. The amount of air pores in matrix can also affect thermal conductivity of this material. This method is proved to be valid and accurate by comparison of numeric and experimental data; the relative error is less than 2%. The method can be used as an effective supplement of theoretical analysis and general FEM calculation for thermal conductivity.

Heat and Mass Transfer in Wet Fibroporous Material Considering Moisture Evaporation

Results of numerical simulation of heat and mass transfer in a wet fibroporous material in conditions of evaporation and steam diffusion were completed. Values of heat and mass fluxes were established. The contribution of evaporation effect to total heat flux and need to consider volume fractions of water and steam into the structure of fibroporous material in calculation of effective thermal conductivity were shown. Nonstationarity of heat and mass transfer in conditions of considered problem can be ignored.

Heat loss of heat pipelines in insulation moisture conditions with the evaporation

Results of numerical simulation of heat and mass transfer in a wet fibroporous material in conditions of evaporation and steam diffusion were obtained. Values of heat and mass fluxes were established. The contribution of evaporation effect to total heat flux and need to consider volume fractions of water and steam into the structure of fibroporous material in calculation of effective thermal conductivity were shown. Nonstationarity of heat and mass transfer in conditions of considered problem can be ignored.

Heat loss of heat pipelines in moisture conditions of thermal insulation

Results of numerical simulation of heat and mass transfer in a wet fibroporous material in conditions of evaporation and steam diffusion were obtained. Values of heat and mass fluxes were established. The contribution of evaporation effect to total heat flux and need to consider volume fractions of water and steam into the structure of fibroporous material in calculation of effective thermal conductivity were shown. Nonstationarity of heat and mass transfer in conditions of considered problem can be ignored.